Former Everton and Manchester City midfielder Jack Rodwell is training with Sheffield United, with Blades boss Chris Wilder saying that "something might develop."
Rodwell is without a club since leaving Blackburn in the summer, after talks about a new contract at Ewood Park broke down.
With the transfer window approaching, clubs in Greece, Australia, America and England – including the Blades – have recently been linked with signing the 28-year-old, who is available on a free transfer.
In the summer of 2018, David McGoldrick was invited to train with Wilder's team when he was without a club, and the striker was offered a contract. The Blades boss is open to the possibility of something similar with Rodwell.
"It's not a trial. Jack is in for a few days," Wilder said. "We know about Jack. He's without a club at the moment after a couple of experiences training (with clubs) in Italy.
"As you've seen in the past, David McGoldrick came in for a few days and Jack is looking at us and we are looking at Jack.
"He is obviously a very, very talented player who obviously should be playing in the Premier League regularly, but for one reason or another isn't.
"He's got a really good attitude and he is in for a few days. It's basically him looking at us and us looking at him to see how he is in terms of how healthy he is.
"But he is obviously a talent because of the team's he's played for and he's looking for a home and it's something that might develop along the way."
Wilder is on record as stating he would like "two or three" new faces in January and on Thursday he went further by saying that defensive-minded players are the priority – a position that Rodwell plays.
"People will try and put two and two together," said Wilder. "Defence and midfield are the main areas, just to strengthen and boost the squad for the second half of the season.
"We need to be strong and have cover and have serious competition. The players have done well so far but we are actively looking.
"We are looking overseas, the foreign market could be one we could look at. From a Premier League point of view, I'm not sure we'd have the finances to go and do that, and we will look at the Championship yet again.
"It probably won't be two or three permanent ones, maybe a bit of a mix, and there's always a loan with an option in the summer. But talks are ongoing talks between myself and the board, we need to lift and invest and hopefully we can make it happen."